Answer:
Yes, the right angle is angle B
Step-by-step explanation:
we have
[tex]A(-2, 3), B(-3,-6),C(2,-1)[/tex]
Plot the vertices
see the attached figure
we know that
If triangle ABC is a right triangle
then
Applying the Pythagoras Theorem
[tex]AB^{2} =AC^{2}+BC^{2}[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(-2, 3), B(-3,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(-1)^{2}}[/tex]
[tex]AB=\sqrt{82}\ units[/tex]
Find the distance BC
[tex]B(-3,-6),C(2,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1+6)^{2}+(2+3)^{2}}[/tex]
[tex]d=\sqrt{(5)^{2}+(5)^{2}}[/tex]
[tex]BC=\sqrt{50}\ units[/tex]
Find the distance AC
[tex]A(-2, 3),C(2,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(2+2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]
[tex]AC=\sqrt{32}\ units[/tex]
Verify the Pythagoras theorem
[tex](\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}[/tex]
[tex]82=82[/tex] ---> is true
therefore
Is a right triangle and the right angle is B
